A fitting system of this type with a fitting designed as a latching fitting on either side is known from DE 10 2009 029 858 A1. The memory device comprises a disk-shaped guide plate fixed on the seat part, a marker disk which is rotatable relative to the guide plate, a disk-shaped toothed plate which is rotatable relative to the marker disk and is fixed on the backrest, and a disk cam which is rotatable by means of a shaft. All of the axes of rotation are aligned with one another and with the pivot axis of the backrest. The guide plate guides a first locking element in the radial direction. The toothed first locking element interacts with a first toothing, facing radially inward, on the marker disk in order to couple the marker disk to the seat part. The marker disk guides a second locking element in the radial direction. The toothed second locking element interacts with a second toothing, facing radially inward, on the toothed plate in order to couple the marker disk to the backrest. The rotating disk cam moves the two locking elements in the radial direction.